Lauren has a total of two hundred seventy pennies, nickels, and quarters. She has a total of $17.10. She has two times as many nickels as quarters and one-third as many quarters as pennies. How many of each coin does she have?

x = number of quarters

2x = number of nickels {two times as many nickels as quarters}

3x = number of pennies {one-third as many quarters as pennies}

0.25x + 0.05(2x) + 0.01(3x) = 17.10 {number of coins times value of coin equals total value}

0.25x + 0.1x + 0.03x = 17.1 {multiplied through}

0.38x = 17.1 {combined like terms}

x = 45 quarters {divided each side by 0.38}

2x = 90 nickels {substituted 45 for x, into 2x}

3x = 135 pennies {substituted 45 for x, into 3x}

**45 quarters, 90 nickels, and 135 pennies**

*- Algebra House*